\documentclass[12pt]{article}
\usepackage[a4paper, margin=2.5cm]{geometry}
\usepackage{ctex}
\usepackage{amsmath, amssymb}
\usepackage{graphicx}
\usepackage{fontspec}
\usepackage{tikz}
\usetikzlibrary{patterns, decorations.pathmorphing}

% 设置中文字体（需 XeLaTeX 或 LuaLaTeX 编译）
\setmainfont{Times New Roman}
\newfontfamily\chinesefont{SimSun} % 使用宋体，可根据系统调整

\title{}
\author{}
\date{}

\begin{document}

\thispagestyle{empty}

% 背景设计
\begin{tikzpicture}[remember picture, overlay]
    % 深蓝色背景
    \fill[blue!45!white] (current page.south west) rectangle (current page.north east);
    
    % 数学元素装饰
    \draw[white!20, thick] (2,-1) circle (3.5);
    \node[white!30] at (2,-1) {$\displaystyle \frac{d^2y}{dx^2} + p(x)\frac{dy}{dx} + q(x)y = 0$};
    
    \draw[white!20, thick] (14,-6) .. controls (12,-4) and (10,-2) .. (8,-1);
    \node[white!30, rotate=-40] at (13,-4) {$y(t) = e^{rt}$};
    
    \draw[white!20, thick] (0,-8) -- (2,-6) -- (4,-7) -- (3,-9) -- cycle;
    \node[white!30] at (2,-7.5) {$\dot{x} = f(x)$};
    
    \draw[white!20, thick, decorate, decoration={snake}] (10,0) -- (13,1);
    \node[white!30] at (12,0) {$\int_\gamma \omega$};

    % 相图示意
    \draw[white!20, ->] (8,-6) .. controls (9,-7) and (10,-6) .. (11,-5);
    \draw[white!20, ->] (11,-5) .. controls (10,-4) and (9,-3) .. (8,-4);
    \node[white!30] at (9.5,-4.5) {相轨线};
\end{tikzpicture}

\vspace*{\fill}
\begin{center}
    {\chinesefont\Huge\bfseries 常微分方程} \\[10pt]
    {\Large\bfseries Ordinary Differential Equations} \\[30pt]
    {\chinesefont\Large 课程讲义} \\[15pt]
    {\Large 数学与应用数学专业} \\[10pt]
    {\Large 2025 年秋季学期} \\[30pt]
    {\Large 主讲教师：\underline{\hspace{4cm}}} \\[10pt]
    {\Large \texttt{contact@math.edu.cn}}
\end{center}
\vspace*{\fill}

\end{document}